1.) Some people believe that Harriet Miers is under-qualified and lacks the experience to be a justice on the Supreme Court because she was never a judge herself, and never argued before the Supreme Court as a lawyer.
2.) Some believe that Harriet Miers is an unacceptable choice because of her ambiguous political philosophy and because of political views she holds that they disagree with.
Bush probably tried to nominate an unknown because of his low public approval ratings. This is the same thing he did when he nominated Roberts as Chief Justice instead on battling for one of the well tested conservatives (Scalia or Thomas). If it turns out that Bush allowed a moderate onto the court's vital swing vote position, he could loose support in Congress and maybe even votes for the Republican Party in the 2006 elections.
The Constitution States that the President "shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the supreme Court".